RLC Resonance, Q Factor and Bandwidth Calculator
Every LC pair rings at one frequency; the resistance decides how enthusiastically. The same three numbers describe a resonant converter tank, an EMI filter pole, an unwanted layout resonance and a snubber problem - only which resistance counts differs. Series and parallel circuits share the frequency and characteristic impedance; the resistance enters upside down between them, which is the single most common RLC mistake.
Choosing something to solve for makes Resonant frequency an editable target and computes the chosen input from it.
Formula
| Z0 | characteristic impedance of the tank (Ohm) |
| Q | quality factor - energy stored over energy lost per radian |
| zeta | damping ratio of the equivalent second-order system |
| tau | ringing envelope decay time constant (s) |
What this model assumes, and where it stops
Assumptions
- Ideal linear L, C and R - no saturation, no bias dependence, no frequency dependence over the band of interest.
- One lumped resistance. Real tanks lose in the winding, the capacitor and the core simultaneously; lump them into one series value at the operating frequency.
- The -3 dB bandwidth and decay expressions assume Q above about 2; heavily damped circuits stop being "resonant" in any useful sense.
- Second-order dynamics only - one L, one C.
Limitations
- Component parasitics move real resonances: a capacitor is inductive above self-resonance and an inductor capacitive, so verify the parts are still themselves at f0.
- Winding resistance rises with frequency through skin and proximity effect, so a Q computed from the DC resistance flatters the tank - sometimes by several times.
- The half-power points sit geometrically around f0, not symmetrically; the bandwidth is exact but its centre shifts visibly below Q of about 5.
- A loaded resonant converter tank sees an effective resistance set by the rectifier and load, not a physical resistor - derive it first (for an LLC, the fundamental-mode approximation), then use this page.
When you need a 3D field solution instead
Closed-form models like the one above hold on idealised geometry. These are the cases where they stop being good enough and a full 3D electromagnetic and thermal solution is the only way to get a trustworthy answer:
- Self-resonance of a real wound component, where turn-to-turn capacitance is a 3D field quantity no lumped model predicts well.
- Busbar and layout resonances in the tens of megahertz, set by loop geometry rather than intentional components.
- Q of a tank at high frequency, where proximity-effect winding loss - a field problem - dominates the resistance.
Common questions
How do I measure Q on the bench?
Two easy ways. Count the visible ring cycles after a step or an injected pulse: the envelope falls to 1/e in Q/pi cycles, so ten visible cycles is a Q of roughly thirty. Or sweep and read the -3 dB width: Q = f0 divided by bandwidth. The two disagree when the resistance is frequency dependent - which for wound components above a few hundred kilohertz it always is.
Why does the resistance act oppositely in series and parallel circuits?
In a series loop the current passes through R every cycle, so bigger R burns more of the stored energy: Q = Z0/R. In a parallel tank the resistor sits across the swing, and a bigger R draws less current from it: Q = R/Z0. Mixing these up inverts the answer by Q^2 - with the default tank that is a factor of 400. When in doubt, convert everything to one topology first.
How do I size an RC snubber from this page?
Read the ringing frequency off the scope, estimate the parasitic L and C from f0 and Z0 (two equations, two unknowns: L = Z0/w0, C = 1/(Z0 w0)), then choose the snubber resistor near that Z0 - this lands the damping ratio near the critical value where ringing dies in about one cycle. The snubber capacitor is typically 3 to 5 times the parasitic C, trading damping speed against dissipation.
References
- Erickson & Maksimovic - Fundamentals of Power Electronics, 3rd ed. - resonant conversion
- Bowick - RF Circuit Design, 2nd ed. - resonant circuits, Q and loaded Q